Overview
In this unit, students will expand upon their knowledge of quadratic functions and equations. This will include graphing and transformations of equations, writing and solving equations in various ways, and modeling real-life situations. It is anticipated that this unit will take from six to eight weeks in a traditional hourly schedule.
Addressed HSCEs
A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate given values of the variables.
A1.1.3 Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities.
A1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.
A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.
A1.2.3 Solve linear and quadratic and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.
A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable. Justify steps in the solution.
A2.1.1 Determine whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function and identify its domain and range.
A2.1.2 Read, interpret, and use function notation and evaluate a function at a value in its domain.
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.
A2.1.6 Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.
A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).
A2.2.1 Combine functions by addition, subtraction, multiplication and division.
A2.2.2 Apply given transformations to parent functions and represent symbolically.
A2.2.3 Determine whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs.
A2.3.2 Describe the tabular pattern associated with functions having constant rate of change (linear) or variable rates of change.
A2.4.2 Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers.
A2.4.3 Using the adapted general symbolic form draw reasonable conclusions about the situation being modeled.
L.1.1.1 Know the different properties that hold in different number systems and recognize that the applicable properties change in the transition from the positive integers to all integers, to the rational numbers, and to real numbers.